Heya, I've been trying to install Mechwarrior 2, the standard DOS version on Windows XP and every time I run the installer, it wants me to create a boot disk as I don't have enough storage space on my C: drive.

I've tried to install the patch, but this hasn't solved the issue.
I've heard that this is a glitch, and I was wondering if creating the boot disk would solve my problem.

Because my pc tower doesn't have a floppy disk drive, I was also considering picking one of these up. Does any one have experience with these, and if so, did it work as well as a standard A: drive?

It depends on your BIOS. Since you said it was an XP computer, it probably does.
If your BIOS has anything about floppies mentioned, it will probably work.
I used one of those for imaging computers as Ghost had a way to set up a floppy for this purpose. Or at least it did in 2007 and later in 2011-2013. I haven't used one since 2013.
At the later job, we did find that the non-IT managers in another building decided to purchase a new model of computer without consulting anyone in IT (salesmen from computer companies generally don't like to deal with the IT department managers, they want to go over their heads to the middle managers who don't know anything about computers so they can bamboozle them) and I recall that that model the floppy would not be recognized with an MS-DOS boot disk because the BIOS did not support floppies. Sorry, I don't recall what model or even make it was. Most were HP computers however.

That USB drive is why computers that don't have a floppy controller on the motherboard will still have something about floppies mentioned in the BIOS.

Wait... Boot Disk... What?!
If I remember right all the boot disk did (for just about any game) was have a boot-up script so when you wanted to play your game all you had to do was insert the boot disk and start/reboot, and it would auto-load the game for you instead of loading to DOS prompt and manually typing it out.
Either way you should not need a Boot Disk to run the game... The default installation is C:/MECH2/MECH2.EXE try looking and see if it installed, if so you should be able to launch the MECH2.EXE file.

I have used the USB Floppy drives in the past, like over a decade ago.
But it boils down to what slickrcbd said, the BIOS will need to support booting from USB (or USB Floppy). Otherwise all you will be able to do is read a floppy disk after windows has booted (which was I was using mine for).

A few games you needed to do a few special configurations, or boot the computer without any TSR programs because they required ALL the UMB and conventional memory.
Sometimes you had to switch from using expanded to extended memory or vice versa, or change config.sys, such as changing between the use of emm386 or himem,
Also for games not compatible with Windows.

These days, you would use DOSbox for any computer running Windows XP or later, you only needed a boot disk for Windows 9X, although before DOSbox, or before DOSbox supported most games, you would still use a boot disk even with XP, actually you were more likely to need it with XP because even more DOS games were incompatible.

One game I recall that was an example of what I was talking about above was "King's Bounty", which is considered the predecessor to the "Heroes of Might and Magic" games, I recall I had to boot without the mouse or CD drivers or there wouldn't be enough memory available [in the lower 1mb] on a computer with 12mb of RAM when the requirements were only 640K (and I got and played King's Bounty on an Apple IIGS with a PC Transporter card that only had 768K of RAM in MS-DOS mode back in 1991). Even using devicehigh did not work, because the memory manager took up too much conventional memory. At least I think it was King's Bounty that was the memory hog.
I wound up putting it on a 3.5" DSDD boot disk and just playing it like most commercial Apple II family games on 5.25" disks where you simply insert the disk and boot the computer. Everything was on the disk and when you are done, eject the disk and reboot.

Hope that clears up why boot disks were once necessary for games, but as I said, anything running Windows XP or later can just use DOSBox. Linux can use DOSbox instead of WINE.
If you're trying to play on a real Windows 9X computer, I can see the necessity. Unless it dual-boots to XP, then you're better off just using DOXbox and XP.
Anything else, not so much anymore.